Output of /home/aschiem/Pgm/Hn/hn --invar -t --shells-10 &K=Q(sqrt(-15)) &Hdim=5 V=K^5 &HNeighbourhood at <2,-1+w> contains 48 classes: mass of the neighbourhood is 31/90 Steinitz class <2,-1+w>: &Hlattice (#1 <-- #41) <1> <1> <1> <2,-1+w> <1> 3 1 3 w 1 3 -1/2w 0 -1 1 -1-w 1-w -1+w 1/2-1/2w 5 |Aut| = 2^4*3^2 #short vectors: 0 0 38 138 336 516 1002 2334 2910 4104 &Hlattice (#2 <-- #43) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 -2+w 4 0 -1+1/2w 1 1/2w 1-1/2w 0 1 -1/2w -1+1/2w 1/2 0 1 |Aut| = 2^5*3^2*5 #short vectors: 0 0 20 210 300 390 1020 2460 3180 3834 &Hlattice (#3 <-- #48) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 3 2-w 4 0 1-1/2w 1 1 1 1/2 1 -1 -1 -1/2 -1/2 1 |Aut| = 2^5*3^2*5 #short vectors: 0 0 20 210 300 390 1020 2460 3180 3834 &Hlattice (#4 <-- #4) <2,-1+w> <1> <1> <2,-1+w> <2,-1+w> 1/2 0 2 0 1 2 0 -1/2w -1/2w 1 0 -1/2w 0 1/2 1 |Aut| = 2^8*3^2 #short vectors: 0 28 2 144 194 600 1056 2432 3216 4344 &Hlattice (#5 <-- #29) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 1 2 0 0 1/2 1 0 0 1 1 1 0 1/2 1 |Aut| = 2^8*3^2 #short vectors: 0 28 2 144 194 600 1056 2432 3216 4344 &Hlattice (#6 <-- #8) <1> <1> <1> <2,-1+w> <1> 2 -1 2 0 -1 2 -1/2w 0 0 1 -1 0 w -1/2-1/2w 5 |Aut| = 2^8*3 #short vectors: 0 26 16 96 240 648 1024 2462 2928 4424 &Hlattice (#7 <-- #47) <1> <1> <1> <1> <2,-1+w> 2 0 2 0 1 2 w -1 0 3 -1 0 0 -1+1/2w 3/2 |Aut| = 2^8*3 #short vectors: 0 26 16 96 240 648 1024 2462 2928 4424 &Hlattice (#8 <-- #9) <2,-1+w> <2,-1+w> <2,-1+w> <2,-1+w> <2,-1+w> 1/2 0 1/2 0 0 1/2 0 0 0 1/2 0 0 0 0 1/2 |Aut| = 2^8*3*5 #short vectors: 0 20 10 160 170 680 1120 1880 3600 4584 &Hlattice (#9 <-- #17) <1> <1> <1> <1> <2,-1+w> 2 0 2 -1 0 2 -w 0 w 3 0 1-1/2w 0 0 1 |Aut| = 2^6*3^2 #short vectors: 0 18 20 120 264 588 1020 2442 2964 4284 &Hlattice (#10 <-- #33) <1> <1> <1> <1> <2,-1+w> 2 0 2 -1 0 2 -1+w 0 1-w 3 0 1-1/2w 0 0 1 |Aut| = 2^6*3^2 #short vectors: 0 18 20 120 264 588 1020 2442 2964 4284 &Hlattice (#11 <-- #31) <2,-1+w> <1> <1> <2,-1+w> <2,-1+w> 1/2 0 2 0 0 2 0 0 1-1/2w 1 0 1-1/2w 0 0 1 |Aut| = 2^6*3^2 #short vectors: 0 16 26 108 266 636 1032 2276 3000 4404 &Hlattice (#12 <-- #11) <1> <2,-1+w> <2,-1+w> <1> <2,-1+w> 2 0 1/2 0 0 1/2 1-w 0 0 3 -1/2w 0 0 1-1/2w 1 |Aut| = 2^7*3 #short vectors: 0 14 28 112 260 656 1048 2138 3096 4464 &Hlattice (#13 <-- #24) <1> <1> <2,-1+w> <1> <1> 2 1 2 -1/2w -1/2w 1 -w 0 1 4 -w 1-w 1 2-w 5 |Aut| = 2^6*3 #short vectors: 0 14 28 108 288 600 1012 2390 2892 4304 &Hlattice (#14 <-- #28) <1> <2,-1+w> <2,-1+w> <1> <2,-1+w> 2 0 1/2 0 0 1/2 -w 0 0 3 1 0 0 1/2w 1 |Aut| = 2^7*3 #short vectors: 0 14 28 112 260 656 1048 2138 3096 4464 &Hlattice (#15 <-- #36) <1> <1> <1> <2,-1+w> <1> 2 -1 2 -1 0 3 0 0 -1+1/2w 1 1-w -1+w -1 -1/2+1/2w 4 |Aut| = 2^6*3 #short vectors: 0 14 28 108 288 600 1012 2390 2892 4304 &Hlattice (#16 <-- #13) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 2 0 w 1 3 0 -1 -1+w -1+w 3 |Aut| = 2^7 #short vectors: 0 12 34 96 290 648 1024 2224 2928 4424 &Hlattice (#17 <-- #27) <1> <1> <1> <1> <2,-1+w> 2 -1 2 0 0 3 1 -1 -2+w 3 0 0 -1-1/2w 1/2w 3/2 |Aut| = 2^4*3 #short vectors: 0 12 38 78 312 648 1002 2322 2766 4404 &Hlattice (#18 <-- #44) <1> <1> <1> <1> <2,-1+w> 2 -1 2 0 0 3 1 -1 -2+w 3 0 0 1 -1/2w 1 |Aut| = 2^5*3 #short vectors: 0 12 36 86 308 634 1004 2336 2796 4374 &Hlattice (#19 <-- #46) <1> <1> <1> <1> <2,-1+w> 2 -1 2 0 0 3 1 -1 1+w 3 0 0 1/2w 1 1 |Aut| = 2^5*3 #short vectors: 0 12 36 86 308 634 1004 2336 2796 4374 &Hlattice (#20 <-- #16) <1> <1> <1> <2,-1+w> <1> 2 0 3 -1+w 0 3 1 -1/2w -1/2w 1 1 w 1-w 0 4 |Aut| = 2^7*3 #short vectors: 0 10 24 144 288 528 1016 2422 3000 4144 &Hlattice (#21 <-- #20) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 -1 3 0 1 -2+w 3 0 1 -1-w -1+w 3 |Aut| = 2^4*3^2 #short vectors: 0 10 38 90 302 654 1020 2198 2892 4434 &Hlattice (#22 <-- #23) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 2 1-w 4 -1/2w 1 1 -1/2w 1-1/2w 1/2 1 -1/2w 1 1/2 1/2 1 |Aut| = 2^8*3*5 #short vectors: 0 10 0 240 240 360 1040 2590 3360 3784 &Hlattice (#23 <-- #30) <1> <2,-1+w> <1> <2,-1+w> <2,-1+w> 2 1 1 -w 1/2-1/2w 4 1 1/2 -1+1/2w 1 1 1/2 1/2w 1/2 1 |Aut| = 2^8*3*5 #short vectors: 0 10 0 240 240 360 1040 2590 3360 3784 &Hlattice (#24 <-- #35) <1> <1> <1> <1> <2,-1+w> 2 0 2 1 -w 3 -w 1 -1 4 0 -1/2w 1 -1/2w 1 |Aut| = 2^7*3 #short vectors: 0 10 24 144 288 528 1016 2422 3000 4144 &Hlattice (#25 <-- #22) <1> <1> <1> <2,-1+w> <1> 2 1 3 -1 -1+w 3 0 -1 1/2w 1 0 -1 -1+w -1/2+1/2w 4 |Aut| = 2^4*3 #short vectors: 0 8 40 90 324 618 1000 2312 2784 4334 &Hlattice (#26 <-- #32) <2,-1+w> <1> <1> <1> <1> 1/2 0 2 0 0 2 0 -1 0 3 0 0 1 -1-w 3 |Aut| = 2^5 #short vectors: 0 8 42 84 314 660 1016 2172 2856 4444 &Hlattice (#27 <-- #38) <1> <1> <1> <2,-1+w> <1> 2 1 3 1 1-w 3 0 1 1/2w 1 0 -w 1 -1 4 |Aut| = 2^4*3 #short vectors: 0 8 40 90 324 618 1000 2312 2784 4334 &Hlattice (#28 <-- #19) <1> <1> <1> <1> <2,-1+w> 2 -w 3 1 0 3 0 -1 1-w 3 -1/2w 1 -1/2w 0 1 |Aut| = 2^6 #short vectors: 0 6 36 116 320 568 1004 2342 2868 4224 &Hlattice (#29 <-- #26) <1> <1> <1> <1> <2,-1+w> 2 1 3 0 1-w 3 0 w -2+w 3 0 1/2w -1 1 3/2 |Aut| = 2^3*3 #short vectors: 0 6 42 92 332 610 998 2300 2778 4314 &Hlattice (#30 <-- #34) <1> <1> <1> <1> <2,-1+w> 2 0 3 -1 1-w 3 -1+w -1 1-w 3 0 -1+1/2w -1 0 1 |Aut| = 2^6 #short vectors: 0 6 36 116 320 568 1004 2342 2868 4224 &Hlattice (#31 <-- #37) <1> <1> <1> <2,-1+w> <1> 2 -1 3 1 -1+w 3 0 1 -1/2w 1 -w 0 -1 -1/2-1/2w 4 |Aut| = 2^6 #short vectors: 0 6 40 100 328 596 1000 2314 2808 4284 &Hlattice (#32 <-- #45) <1> <1> <1> <1> <2,-1+w> 2 w 3 1 1-w 3 0 -1 -1 3 1-1/2w -1-1/2w -1/2w 1 3/2 |Aut| = 2^6 #short vectors: 0 6 40 100 328 596 1000 2314 2808 4284 &Hlattice (#33 <-- #40) <2,-1+w> <1> <1> <1> <1> 1 -1 4 -1/2+1/2w -1-w 4 0 w -1-w 4 -1/2-1/2w -1+w -1 1+w 4 |Aut| = 2^5*3 #short vectors: 0 4 36 126 324 546 1004 2344 2892 4174 &Hlattice (#34 <-- #42) <1> <1> <1> <1> <2,-1+w> 2 -1 3 -w 1 4 1 -w w 4 0 -1/2w 0 1 1 |Aut| = 2^5*3 #short vectors: 0 4 36 126 324 546 1004 2344 2892 4174 &Hlattice (#35 <-- #1) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 1 0 0 0 0 1/2 |Aut| = 2^8*3 #short vectors: 8 28 66 152 322 544 992 1984 2904 3904 &Hlattice (#36 <-- #5) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 1 0 0 0 2 0 0 0 1-1/2w 1 |Aut| = 2^6*3^2 #short vectors: 6 18 56 174 336 462 984 2190 2910 3774 &Hlattice (#37 <-- #2) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 1 0 0 1/2 0 0 0 1/2 0 0 0 0 1/2 |Aut| = 2^7*3 #short vectors: 4 16 54 132 294 636 1040 1828 3108 4284 &Hlattice (#38 <-- #6) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 2 0 0 -1 3 0 0 -1/2w -1+1/2w 1 |Aut| = 2^7*3 #short vectors: 4 10 48 180 336 444 992 2254 2964 3804 &Hlattice (#39 <-- #14) <1> <1> <1> <1> <2,-1+w> 1 0 1 0 0 2 0 0 w 3 0 0 -1 -1+1/2w 1 |Aut| = 2^7*3 #short vectors: 4 10 48 180 336 444 992 2254 2964 3804 &Hlattice (#40 <-- #3) <1> <1> <1> <2,-1+w> <1> 1 0 2 0 -1 2 0 0 0 1/2 0 w -w 0 3 |Aut| = 2^6*3 #short vectors: 2 16 42 110 298 622 1016 2164 2922 4294 &Hlattice (#41 <-- #7) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 -1 2 0 -1 0 4 0 -1/2w 1/2w 1 1 |Aut| = 2^6*3 #short vectors: 2 14 40 126 312 558 1000 2306 2874 4134 &Hlattice (#42 <-- #10) <1> <1> <2,-1+w> <2,-1+w> <2,-1+w> 1 0 2 0 0 1/2 0 0 0 1/2 0 1-1/2w 0 0 1 |Aut| = 2^6*3 #short vectors: 2 14 44 114 292 642 1032 2026 3018 4354 &Hlattice (#43 <-- #12) <1> <1> <1> <2,-1+w> <1> 1 0 2 0 -1 2 0 0 0 1/2 0 1-w -1+w 0 3 |Aut| = 2^6*3 #short vectors: 2 16 42 110 298 622 1016 2164 2922 4294 &Hlattice (#44 <-- #15) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 1-w 3 0 -w 2-w 4 0 1 1/2w 1/2w 1 |Aut| = 2^6*3 #short vectors: 2 6 40 166 328 470 1000 2314 2970 3934 &Hlattice (#45 <-- #18) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 -w 3 0 1 -1 3 0 -1/2w 1 -1/2w 1 |Aut| = 2^6*3 #short vectors: 2 6 40 166 328 470 1000 2314 2970 3934 &Hlattice (#46 <-- #21) <1> <1> <1> <1> <2,-1+w> 1 0 2 0 -1 2 0 1 -1 2 0 -1 1 -1+1/2w 3/2 |Aut| = 2^5*3*5 #short vectors: 2 20 40 96 300 624 1000 2300 2802 4284 &Hlattice (#47 <-- #25) <1> <1> <1> <2,-1+w> <1> 1 0 2 0 1 2 0 0 1 1 0 -1+w w 1/2+1/2w 4 |Aut| = 2^6*3 #short vectors: 2 14 40 126 312 558 1000 2306 2874 4134 &Hlattice (#48 <-- #39) <1> <1> <1> <1> <2,-1+w> 1 0 3 0 w 3 0 -1+w w 3 0 1/2w 0 1 1 |Aut| = 2^5*3*5 #short vectors: 2 0 40 196 340 404 1000 2320 3042 3784 &Adjacence matrix (M_ij=#{neighbours of class i isometric to class j}): 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 9 0 6 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 15 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 0 12 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 1 0 3 0 0 0 0 0 0 12 0 0 0 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 4 0 0 6 0 0 0 0 16 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 8 12 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 5 0 0 0 0 0 10 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 12 0 0 0 0 0 0 0 0 0 0 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 18 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 6 0 1 0 0 0 0 9 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 9 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 2 0 0 0 1 0 0 0 2 0 0 6 0 0 0 0 0 0 0 0 1 0 12 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 6 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 3 0 0 0 0 8 0 0 0 0 0 8 0 0 0 0 0 0 0 6 0 0 0 0 0 0 1 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 4 0 2 0 6 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 0 0 4 0 0 3 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 6 0 0 0 4 0 0 0 0 0 0 0 0 6 0 0 0 12 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 2 0 0 0 0 2 2 0 0 0 1 0 0 0 0 0 0 0 1 0 8 8 0 0 2 2 0 0 0 0 0 1 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 1 0 0 0 4 4 1 0 0 0 0 0 6 6 4 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 2 0 8 0 0 0 0 0 0 6 0 0 4 0 6 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 8 1 0 0 6 0 0 0 0 0 0 0 8 6 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 1 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 16 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 9 0 0 1 0 0 0 0 9 3 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 20 0 0 0 0 16 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 4 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 12 0 0 0 6 0 0 0 0 1 0 0 0 0 0 0 0 0 0 6 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 3 4 0 0 0 1 0 0 0 0 0 3 0 12 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 4 0 4 0 4 0 0 0 0 11 0 1 6 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 0 6 0 0 0 0 0 0 0 2 3 0 3 2 0 6 6 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 4 0 0 1 0 4 0 0 0 0 0 0 0 0 0 0 0 2 4 8 0 0 0 0 0 0 0 0 0 1 0 2 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 2 1 0 0 0 0 0 1 3 6 3 6 0 0 3 0 3 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 4 2 0 0 8 0 0 0 8 2 0 0 0 0 1 0 0 0 1 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 8 2 0 0 8 8 0 1 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 4 0 0 0 0 0 8 0 4 0 0 4 4 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 4 0 0 0 3 12 0 0 0 0 6 0 0 0 0 0 0 3 0 0 0 0 0 0 2 4 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 2 0 0 0 0 0 6 12 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 3 0 0 0 0 0 0 0 1 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 4 6 6 0 4 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 3 0 0 9 0 0 3 0 0 9 0 0 0 0 0 0 0 0 0 0 1 0 0 0 3 0 0 0 3 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 5 0 1 0 0 6 6 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 0 0 0 0 0 0 0 6 1 2 0 0 0 0 0 12 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 0 4 0 3 0 0 4 2 0 0 0 0 0 0 0 6 8 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 4 0 0 0 4 0 0 3 0 0 0 0 0 0 0 0 3 0 0 2 0 0 4 0 3 4 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 0 0 3 8 0 0 0 0 0 0 0 0 3 0 1 1 3 0 0 0 0 8 0 0 0 0 0 0 0 0 0 0 1 2 0 0 3 0 0 0 0 0 0 0 0 0 0 0 6 0 0 0 3 0 0 0 0 0 1 3 0 0 6 0 3 0 0 0 0 3 0 0 0 0 0 1 0 0 0 0 1 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 6 0 0 0 0 6 0 0 0 1 0 0 0 0 0 6 6 2 0 0 0 1 0 8 0 0 0 0 0 0 0 0 0 0 0 0 0 3 0 0 0 0 0 0 0 1 0 0 0 0 0 0 3 0 0 0 0 0 3 0 0 1 0 0 0 3 1 8 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 6 0 0 6 0 0 0 1 0 6 0 6 0 0 0 1 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 0 0 0 0 0 0 0 10 0 0 0 0 0 0 0 0 0 0 0 0 0 5 0 10 0 0 1 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 0 0 0 0 0 2 0 0 0 0 0 0 0 0 0 0 0 0 6 0 6 1 0 0 0 0 6 0 0 0 6 0 2 1 0 0 0 5 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 10 0 0 0 10 0 0 0 0 0 5 0 0 0 1 classes of Z-lattices with respect to the trace form &Dim=10 V=Q^10 &Genus of the trace-forms: det= 759375 = 3^5 *5^5 2-adic symbol: 1^10_II 5-adic symbol: 1^5 5^-5 3-adic symbol: 1^5 3^-5 -1-adic symbol: +^10 -^0 level=15, weight=5 a_0,..,a_20 determine modular form &Gram (#1 <- H1) 6 2 6 2 2 6 0 2 -2 6 1 2 2 -2 6 0 -2 2 -2 2 6 2 2 1 1 1 -1 6 2 3 0 3 0 0 2 8 2 3 0 0 3 0 2 -1 8 3 -1 3 -2 -1 2 2 -2 1 8 |Aut| = 2^5*3^2 #short vectors: 0 0 0 0 0 38 0 138 0 336 0 516 0 1002 0 2334 0 2910 0 4104 &Gram (#2 <- H2,H3) 6 2 6 2 -2 6 2 2 -2 6 2 2 2 2 6 3 -1 2 -1 -1 8 2 2 2 1 1 -2 8 1 2 1 -2 2 -1 -1 8 2 -2 3 -2 -1 4 -2 -1 8 1 -2 1 -2 -3 0 1 2 0 8 |Aut| = 2^5*3^2*5 #short vectors: 0 0 0 0 0 20 0 210 0 300 0 390 0 1020 0 2460 0 3180 0 3834 &Gram (#3 <- H4,H5) 4 1 4 0 0 4 0 0 -2 4 0 0 2 -2 4 0 0 2 0 2 4 0 0 -1 0 -1 -1 8 0 0 0 1 0 0 -4 8 0 0 0 0 -1 -1 4 0 8 0 0 1 0 0 1 -4 0 0 8 |Aut| = 2^9*3^2 #short vectors: 0 0 0 28 0 2 0 144 0 194 0 600 0 1056 0 2432 0 3216 0 4344 &Gram (#4 <- H6,H7) 4 0 4 0 2 4 0 -2 0 4 0 -2 0 0 4 1 2 0 0 -2 6 0 -1 -1 1 0 0 8 2 2 1 0 -1 2 -4 10 2 2 0 -1 -2 2 -4 2 10 2 1 -1 -2 -1 1 -4 1 2 10 |Aut| = 2^8*3 #short vectors: 0 0 0 26 0 16 0 96 0 240 0 648 0 1024 0 2462 0 2928 0 4424 &Gram (#5 <- H8) 4 0 4 0 0 4 0 0 0 4 0 0 0 0 4 -1 0 0 0 0 4 0 -1 0 0 0 0 4 0 0 -1 0 0 0 0 4 0 0 0 -1 0 0 0 0 4 0 0 0 0 -1 0 0 0 0 4 |Aut| = 2^13*3*5 #short vectors: 0 0 0 20 0 10 0 160 0 170 0 680 0 1120 0 1880 0 3600 0 4584 &Gram (#6 <- H9,H10) 4 2 4 2 2 4 0 0 0 4 0 0 0 2 4 0 0 0 1 -1 6 0 0 0 -2 -1 2 6 1 0 0 0 0 0 0 6 1 1 1 0 0 0 0 2 6 0 0 1 0 0 0 0 -2 2 6 |Aut| = 2^7*3^2 #short vectors: 0 0 0 18 0 20 0 120 0 264 0 588 0 1020 0 2442 0 2964 0 4284 &Gram (#7 <- H11) 4 1 4 0 0 4 0 0 -2 4 0 0 0 0 4 0 0 0 0 -2 4 0 0 0 0 -1 2 6 0 0 0 0 1 1 -2 6 0 0 1 -2 0 0 0 0 6 0 0 -2 1 0 0 0 0 2 6 |Aut| = 2^9*3^2 #short vectors: 0 0 0 16 0 26 0 108 0 266 0 636 0 1032 0 2276 0 3000 0 4404 &Gram (#8 <- H12,H14) 4 0 4 0 -1 4 0 0 0 4 0 0 0 -1 4 0 0 0 0 0 4 0 0 0 0 0 0 4 1 0 0 0 0 2 2 6 2 0 0 0 0 2 1 2 6 2 0 0 0 0 1 2 2 2 6 |Aut| = 2^9*3 #short vectors: 0 0 0 14 0 28 0 112 0 260 0 656 0 1048 0 2138 0 3096 0 4464 &Gram (#9 <- H13,H15) 4 2 4 2 2 4 0 0 0 4 2 0 2 -2 6 0 0 0 1 1 6 2 2 0 2 -1 -2 8 1 0 0 0 -1 -2 3 8 0 -1 0 0 2 2 -3 0 8 0 0 1 0 -1 -2 2 0 0 8 |Aut| = 2^6*3 #short vectors: 0 0 0 14 0 28 0 108 0 288 0 600 0 1012 0 2390 0 2892 0 4304 &Gram (#10 <- H16) 4 1 4 0 0 4 0 0 0 4 0 0 0 0 4 0 0 0 0 0 4 0 0 1 2 2 0 6 0 0 2 -1 0 2 0 6 0 0 -2 0 1 2 0 0 6 0 0 0 -2 -2 -1 -2 0 -1 6 |Aut| = 2^9 #short vectors: 0 0 0 12 0 34 0 96 0 290 0 648 0 1024 0 2224 0 2928 0 4424 &Gram (#11 <- H17) 4 2 4 2 2 4 2 2 0 6 2 0 0 2 6 2 2 2 2 -1 6 2 2 2 1 2 0 6 1 0 0 -1 -1 0 -2 8 1 1 1 2 2 1 3 0 8 0 0 1 1 0 2 -2 2 -2 8 |Aut| = 2^5*3 #short vectors: 0 0 0 12 0 38 0 78 0 312 0 648 0 1002 0 2322 0 2766 0 4404 &Gram (#12 <- H18,H19) 4 2 4 2 0 4 2 2 0 6 2 0 2 -1 6 2 2 0 2 2 6 2 0 2 2 0 -1 6 1 2 -1 0 -1 0 -1 8 1 -1 2 1 2 1 2 0 8 2 1 0 0 0 0 0 0 1 8 |Aut| = 2^5*3 #short vectors: 0 0 0 12 0 36 0 86 0 308 0 634 0 1004 0 2336 0 2796 0 4374 &Gram (#13 <- H20,H24) 4 0 4 0 0 4 0 0 0 4 0 0 0 0 4 1 0 -2 -2 0 6 0 -1 2 -2 0 0 6 0 0 -2 -2 -1 2 0 6 2 -2 1 -2 2 1 2 0 8 2 -2 2 1 2 -1 1 -2 3 8 |Aut| = 2^7*3 #short vectors: 0 0 0 10 0 24 0 144 0 288 0 528 0 1016 0 2422 0 3000 0 4144 &Gram (#14 <- H21) 4 1 4 0 0 4 0 0 -2 4 0 0 -2 2 6 0 0 2 -2 1 6 0 0 -2 2 2 0 6 0 0 2 0 -2 0 -3 6 0 0 -1 0 -2 -1 -2 0 8 0 0 1 -1 -3 -1 1 1 2 8 |Aut| = 2^6*3^2 #short vectors: 0 0 0 10 0 38 0 90 0 302 0 654 0 1020 0 2198 0 2892 0 4434 &Gram (#15 <- H22,H23) 4 0 4 0 0 4 0 0 0 4 0 0 0 0 4 1 2 2 2 2 8 2 -1 2 2 -2 1 8 2 2 -1 2 -2 1 2 8 2 2 2 2 1 4 2 2 8 2 2 2 1 2 4 1 1 4 8 |Aut| = 2^8*3*5 #short vectors: 0 0 0 10 0 0 0 240 0 240 0 360 0 1040 0 2590 0 3360 0 3784 &Gram (#16 <- H25,H27) 4 2 4 0 0 4 2 0 2 6 2 0 -2 0 6 2 2 0 1 2 6 2 2 0 2 1 2 6 0 0 1 0 0 2 -2 6 1 1 0 2 2 3 3 0 8 0 1 0 -2 -2 -2 -2 0 0 8 |Aut| = 2^4*3 #short vectors: 0 0 0 8 0 40 0 90 0 324 0 618 0 1000 0 2312 0 2784 0 4334 &Gram (#17 <- H26) 4 1 4 0 0 4 0 0 0 4 0 0 2 2 6 0 0 -2 0 1 6 0 0 2 -2 0 -2 6 0 0 0 -2 -2 0 -1 6 0 0 -1 0 0 -1 -1 2 6 0 0 0 -1 0 2 1 2 0 6 |Aut| = 2^7 #short vectors: 0 0 0 8 0 42 0 84 0 314 0 660 0 1016 0 2172 0 2856 0 4444 &Gram (#18 <- H28,H30) 4 0 4 0 0 4 2 2 0 6 2 -2 0 0 6 0 0 -2 -2 -1 6 0 0 2 1 2 -2 6 1 0 0 1 0 -2 -2 6 0 0 1 2 2 -2 2 0 6 0 1 0 1 -1 -2 -2 2 0 6 |Aut| = 2^6 #short vectors: 0 0 0 6 0 36 0 116 0 320 0 568 0 1004 0 2342 0 2868 0 4224 &Gram (#19 <- H29) 4 2 4 2 2 6 2 2 0 6 2 0 2 2 6 2 0 2 1 2 6 2 0 2 0 1 0 6 0 0 1 0 -2 2 -1 6 1 -1 0 1 2 2 0 -2 8 1 2 1 2 1 1 -1 -2 -1 8 |Aut| = 2^4*3 #short vectors: 0 0 0 6 0 42 0 92 0 332 0 610 0 998 0 2300 0 2778 0 4314 &Gram (#20 <- H31,H32) 4 0 4 0 0 4 2 2 0 6 0 -2 2 -2 6 0 2 2 1 0 6 2 2 0 2 -1 2 6 0 0 -1 -2 0 -1 -2 6 1 0 0 1 -2 -2 0 0 6 2 1 0 0 -2 -1 3 0 2 8 |Aut| = 2^6 #short vectors: 0 0 0 6 0 40 0 100 0 328 0 596 0 1000 0 2314 0 2808 0 4284 &Gram (#21 <- H33,H34) 4 0 4 2 -2 6 2 -2 2 6 0 0 2 2 6 2 -2 2 2 -1 6 0 0 -2 1 0 -2 6 0 0 1 -2 -1 2 -2 6 1 2 -1 0 -2 0 2 -2 8 2 1 1 0 2 0 -2 2 -2 8 |Aut| = 2^5*3 #short vectors: 0 0 0 4 0 36 0 126 0 324 0 546 0 1004 0 2344 0 2892 0 4174 &Gram (#22 <- H35) 2 0 2 0 0 2 0 0 0 2 0 0 0 0 4 0 0 0 0 -1 4 1 0 0 0 0 0 8 0 -1 0 0 0 0 0 8 0 0 -1 0 0 0 0 0 8 0 0 0 -1 0 0 0 0 0 8 |Aut| = 2^13*3 #short vectors: 0 8 0 28 0 66 0 152 0 322 0 544 0 992 0 1984 0 2904 0 3904 &Gram (#23 <- H36) 2 0 2 0 0 2 0 0 0 4 0 0 0 2 4 0 0 0 -1 1 6 0 0 0 1 2 -2 6 1 0 0 0 0 0 0 8 0 1 0 0 0 0 0 0 8 0 0 1 0 0 0 0 0 0 8 |Aut| = 2^10*3^2 #short vectors: 0 6 0 18 0 56 0 174 0 336 0 462 0 984 0 2190 0 2910 0 3774 &Gram (#24 <- H37) 2 0 2 0 0 4 0 0 -1 4 0 0 0 0 4 0 0 0 0 -1 4 0 0 0 0 0 0 4 0 0 0 0 0 0 -1 4 1 0 0 0 0 0 0 0 8 0 -1 0 0 0 0 0 0 0 8 |Aut| = 2^12*3 #short vectors: 0 4 0 16 0 54 0 132 0 294 0 636 0 1040 0 1828 0 3108 0 4284 &Gram (#25 <- H38,H39) 2 0 2 0 0 4 0 0 0 4 0 0 0 0 4 0 0 1 2 2 6 0 0 2 2 -1 1 6 0 0 2 -1 2 1 0 6 1 0 0 0 0 0 0 0 8 0 -1 0 0 0 0 0 0 0 8 |Aut| = 2^9*3 #short vectors: 0 4 0 10 0 48 0 180 0 336 0 444 0 992 0 2254 0 2964 0 3804 &Gram (#26 <- H40,H43) 2 0 4 0 -2 4 0 2 -2 4 0 0 0 0 4 0 0 0 0 -1 4 0 1 -1 1 0 0 6 0 -1 0 0 0 0 -2 6 0 0 -1 0 0 0 2 2 6 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^8*3 #short vectors: 0 2 0 16 0 42 0 110 0 298 0 622 0 1016 0 2164 0 2922 0 4294 &Gram (#27 <- H41,H47) 2 0 4 0 -2 4 0 2 0 4 0 0 0 0 4 0 2 0 0 -1 6 0 2 -2 1 2 0 8 0 -1 -1 -2 -2 0 -3 8 0 -2 1 0 2 -2 2 1 8 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^7*3 #short vectors: 0 2 0 14 0 40 0 126 0 312 0 558 0 1000 0 2306 0 2874 0 4134 &Gram (#28 <- H42) 2 0 4 0 -2 4 0 0 0 4 0 0 0 -1 4 0 0 0 0 0 4 0 0 0 0 0 -1 4 0 -1 2 0 0 0 0 6 0 1 1 0 0 0 0 -2 6 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^10*3 #short vectors: 0 2 0 14 0 44 0 114 0 292 0 642 0 1032 0 2026 0 3018 0 4354 &Gram (#29 <- H44,H45) 2 0 4 0 0 4 0 0 0 4 0 2 2 2 6 0 -1 0 0 -2 6 0 1 0 0 -1 -2 6 0 0 -1 0 -2 2 2 6 0 -2 -2 1 0 1 0 1 8 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^7*3 #short vectors: 0 2 0 6 0 40 0 166 0 328 0 470 0 1000 0 2314 0 2970 0 3934 &Gram (#30 <- H46) 2 0 4 0 -2 4 0 2 -2 4 0 -2 0 0 4 0 -2 0 -1 0 8 0 -1 2 0 -1 2 8 0 -1 -1 -1 2 2 -3 8 0 2 -1 0 0 0 -3 -1 8 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^7*3*5 #short vectors: 0 2 0 20 0 40 0 96 0 300 0 624 0 1000 0 2300 0 2802 0 4284 &Gram (#31 <- H48) 2 0 6 0 2 6 0 2 -2 6 0 2 2 -2 6 0 1 2 1 2 6 0 1 -1 0 2 2 6 0 2 -1 1 1 -2 2 6 0 2 0 1 2 -1 2 2 6 1 0 0 0 0 0 0 0 0 8 |Aut| = 2^7*3*5 #short vectors: 0 2 0 0 0 40 0 196 0 340 0 404 0 1000 0 2320 0 3042 0 3784